Elastic properties of materials used in many fields are often critical to the design, operation, or safety of the materials. In the field of manufacturing, the elastic properties of manufactured materials and their components often must meet defined specifications which are essential to the utility and safety of the manufactured products. In the medical field, elastic properties of biological tissues are important for tissue function. In the field of construction, the elastic properties of construction materials including foundation soils are important to the design criteria and safety considerations for engineered structures, roads, dams, excavations, and earthworks. In all these fields, it is useful and often essential to have an efficient, reliable means to obtain elastic properties of the materials in question. For medical applications, it is often desirable that the method be non-destructive and be based on in vivo diagnostic data.
Current techniques used to measure the properties of material sheets suffer from two deficiencies. First, currently measurement techniques are usually invasive and destructive and therefore not ideal for in vivo measurements. Second, existing techniques only measure overall (average) properties over the material specimen, thus failing to account for the heterogeneous distribution of properties.
In general, the stress in a deformable solid depends on the applied load, displacement constraints, geometry, and material property. There is, nevertheless, a class of problems in which the stress depends only on the load, boundary condition and geometry, but not the material property. Systems as such are called statically determined. Static determinacy plays a crucial role in experimental characterization of elastic properties, because in a statically determined system the stress can be obtained without knowing the material properties in question. The stress data acquired from equilibrium, together with the strain date computed from measured deformation, finishes the data base for quantifying the material property. The classical material characterization method, the specimen test, makes use of uniform stress which is a fundamental type of statically determined stress field. This invention hinges on another family of static determinate system, the membrane structure load by transverse pressure. Static determinacy in membrane structures has long been long recognized. For example, it is known that the wall tension in a pressurized spherical membrane follows the Laplace formula T=pR/2 (T: wall tension, p: transmural pressure, R: inner radius) in which the material property plays no role. Static determinacy in membranes stems from the characteristics of membrane equilibrium. A membrane is a thin material body of which the thickness is much smaller than the other dimensions. Due to thinness, a membrane has negligible resistance to bending and transverse shear. Thus, the stress is locally in a plane stress state, having three nonzero components. When the membrane surface is curved, the equilibrium equation gives rise to three component equations. Thus, the equilibrium equations are closed. If the membrane is subjected to traction boundary alone (Neumann problem), the wall stress is completely independent of the material properties. When displacement boundary conditions are present (Dirichlet or mixed problems), the equilibrium equations are no longer closed and stress solution requires the knowledge of material's stress-strain relation (constitutive equation). However, if the membrane is sufficiently deep (say the height is comparable to the diameter), the influence of material exists only in a thin boundary layer; the far field stress is asymptotic to the material-independent static distribution. Thus, for practical purposes, curved membranes can be viewed as statically determinate even at the presence of boundary constants.
What is needed is a non-invasive and non-destructive system and methods that can identify material properties such as those in anisotropic heterogeneous nonlinear, elastic materials. The present invention satisfies this demand.